PolynomialRegression/Polynomial Regression.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Algorytm najszybszego spadku dla regresji wielomianowej. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Skład grupy:\n",
    "- Nowak Ania,\n",
    "- Łaźna Patrycja,\n",
    "- Bregier Damian"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import random\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "np.set_printoptions(suppress=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 0. Podstawowe informacje o zbiorze danych"
   ]
  },
  {
   "attachments": {
    "image.png": {
     "image/png": "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
    }
   },
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Ze względu na specyfikę wytycznych projektu zakładającego wykorzystanie jedynie dwóch cech: x i y oraz modelowanie zależności y od x za pomocą funkcji wielomianowej dobrany został przez nas odpowiedni dataset. Obejmuje on jedynie trzy kolumny, czyli: płeć, wzrost w calach oraz wagę w funtach, z czego ze względu na specyfikę projektu wykorzystywane są jedynie wzrost oraz waga. Każdy z parametrów zawiera po 10 tysięcy unikalnych wartości.\n",
    "\n",
    "![image.png](attachment:image.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 1. Wczytywanie i preprocessing danych"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Stopień wielomianu\n",
    "degree = 4\n",
    "X_plot = np.linspace(0, 100, 1000)\n",
    "initial_theta = np.matrix([0] * (degree + 1)).reshape(degree + 1, 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Wybór dwóch kolumn - dotyczących wzrostu i wagi\n",
    "data = pd.read_csv('weight-height.csv')[[\"Height\", \"Weight\"]]\n",
    "# Czyszczenie tabeli i wartości pustych\n",
    "data = data.dropna()\n",
    "data_matrix = np.matrix(data)\n",
    "\n",
    "m, n_plus_1 = data_matrix.shape\n",
    "n = n_plus_1 - 1\n",
    "X = (np.ones((m, 1)))\n",
    "\n",
    "for i in range(1, degree + 1):\n",
    "    Xn = np.power(data_matrix[:, 0:n], i)\n",
    "    Xn /= np.amax(Xn, axis=0)\n",
    "    X = np.concatenate((X, Xn), axis=1)\n",
    "\n",
    "X = np.matrix(X).reshape(m, degree * n + 1)\n",
    "Y = np.matrix(data_matrix[:, -1])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2. Metody do regresji wielomianowej"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "# Implementacja wzrosu na regresję wielomianową\n",
    "def polynomial_regression(theta, x):\n",
    "    x = x/data[\"Height\"].max()\n",
    "    return sum(theta * np.power(x, i) for i, theta in enumerate(theta.tolist()))\n",
    "\n",
    "# Implementacja wzoru na RMSE, czyli pierwiastek z błędu średniokwadratowego\n",
    "def mean_squared_error(theta, X, Y):\n",
    "    J = 1.0 / (2.0 * m) * ((X * theta - Y).T * (X * theta - Y))\n",
    "    return J.item()\n",
    "\n",
    "# Wzór na gradient prosty\n",
    "def gradient(theta, X, Y):\n",
    "    return 1.0 / len(Y) * (X.T * (X * theta - Y)) \n",
    "\n",
    "# Batch gradient descent (BGD)\n",
    "def BGD(X, Y, theta, cost_function = mean_squared_error, alpha=0.1, eps=10**-5, max_steps = 10000000000):\n",
    "    cost = cost_function(theta, X, Y)\n",
    "    logs = [[cost, theta]]\n",
    "    \n",
    "    for i in range(max_steps):\n",
    "        theta = theta - alpha * gradient(theta, X, Y)\n",
    "        next_cost = cost_function(theta, X, Y)\n",
    "        logs.append([next_cost, theta])\n",
    "        if abs(cost - next_cost) <= eps:\n",
    "            break\n",
    "        cost = next_cost\n",
    "    return theta, logs\n",
    "\n",
    "# Batch gradient descent (BGD)\n",
    "def steepest_descent(X, Y, theta, cost_function = mean_squared_error, eps=10**-5, max_steps = 10000000000):\n",
    "    cost = cost_function(theta, X, Y)\n",
    "    logs = [[cost, theta]]\n",
    "    \n",
    "    for i in range(max_steps):\n",
    "        theta = theta - alpha * gradient(theta, X, Y)\n",
    "        next_cost = cost_function(theta, X, Y)\n",
    "        logs.append([next_cost, theta])\n",
    "        if abs(cost - next_cost) <= eps:\n",
    "            break\n",
    "        cost = next_cost\n",
    "    return theta, logs\n",
    "\n",
    "# Mini-batch gradient descent (MBGD)\n",
    "def MBGD(X, Y, theta, cost_function = mean_squared_error, alpha=0.1, epochs=5, batch_size=16):\n",
    "    cost = cost_function(theta, X, Y)\n",
    "    logs = [[cost, theta]]\n",
    "    start, end = 0, batch_size\n",
    "    \n",
    "    steps = m / batch_size\n",
    "    for i in range(epochs):\n",
    "        zipped_XY = list(zip(X, Y))\n",
    "        random.shuffle(zipped_XY)\n",
    "        X_shuffled, Y_shuffled = zip(*zipped_XY)\n",
    "        X_shuffled = np.concatenate(X_shuffled, axis=0) \n",
    "        Y_shuffled = np.concatenate(Y_shuffled, axis=0) \n",
    "        for j in range(int(steps)):\n",
    "            batch =  X_shuffled[start:end,:], Y_shuffled[start:end,:]\n",
    "            theta = theta - alpha * gradient(theta, batch[0], batch[1])\n",
    "            cost = cost_function(theta, X, Y)\n",
    "            logs.append([cost, theta])\n",
    "\n",
    "            if start + batch_size < batch_size:\n",
    "                start += batch_size\n",
    "            else:\n",
    "                start = 0\n",
    "            end = min(start + batch_size, m)\n",
    "    return theta, logs\n",
    "\n",
    "# Stochastic gradient descent (SGD)\n",
    "def SGD(X, Y, theta, cost_function = mean_squared_error, alpha=0.1, epochs=5, batch_size=16):\n",
    "    return MBGD(X, Y, theta, gradient, cost_function, alpha, epochs, 1)\n",
    "\n",
    "#print(mean_squared_error([1,2,1,1],[1,2,43,1]))\n",
    "#mean_squared_error(polynomial_regression(initial_theta, X), Y)\n",
    "#final_theta, logs_1 = BGD(X, Y, initial_theta)\n",
    "final_theta, logs_2 = MBGD(X, Y, initial_theta, epochs = 30, batch_size = 16)\n",
    "#final_theta, logs_2 = SGD(X, Y, initial_theta, epochs = 30)"
   ]
  },
  {
   "attachments": {
    "image.png": {
     "image/png": "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
    }
   },
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Metoda gradientu prostego\n",
    "![image.png](attachment:image.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 3. Reprezentacja graficzna regresji wielomianowej"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": "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
      "text/plain": [
       "<Figure size 720x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "def plot_polynomial_regression(theta):\n",
    "    fig = plt.figure(figsize=(10,5))\n",
    "    Y_plot = polynomial_regression(theta, X_plot).tolist()\n",
    "    chart = fig.add_subplot()\n",
    "    chart.plot(data[\"Height\"], Y ,\"go\")\n",
    "    chart.plot(X_plot, Y_plot, color=\"red\", lw=2, label=f\"degree {len(theta)}\")\n",
    "    plt.ylim([0,250])\n",
    "    plt.show()\n",
    "    \n",
    "#plot_polynomial_regression(initial_theta)\n",
    "plot_polynomial_regression(final_theta)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-33.70007165990287x^0 + 36.22536357022561x^1 + 77.13438753083798x^2 + 97.31645980974973x^3 + 103.01308458334519x^4 + "
     ]
    }
   ],
   "source": [
    "for i,x in enumerate(final_theta.tolist()):\n",
    "    x = x[0]\n",
    "    print(f\"{x}x^{i}\", end=\" + \")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 4. Regresja wielomianowa z wykorzystaniem gotowej biblioteki"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.preprocessing import PolynomialFeatures, StandardScaler\n",
    "from sklearn.pipeline import make_pipeline\n",
    "from sklearn.linear_model import Ridge, LinearRegression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Pipeline(steps=[('polynomialfeatures', PolynomialFeatures(degree=4)),\n",
       "                ('linearregression', LinearRegression())])"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model = make_pipeline(PolynomialFeatures(degree=degree, include_bias=True), \n",
    "                       LinearRegression())\n",
    "model.fit(data[[\"Height\"]],Y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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
      "text/plain": [
       "<Figure size 720x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "Y_plot_2 = model.predict([[x] for x in X_plot])\n",
    "\n",
    "fig = plt.figure(figsize=(10,5))\n",
    "chart = fig.add_subplot()\n",
    "chart.plot(data[\"Height\"], Y ,\"go\")\n",
    "chart.plot(X_plot, Y_plot_2, color=\"red\", lw=2, label=f\"degree {degree}\")\n",
    "plt.ylim([0,250])\n",
    "plt.xlim([0,100])\n",
    "degree"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}